Struct RationalFunctionField 

pub struct RationalFunctionField<R: Field> { /* private fields */ }

The rational function field R(t) over a coefficient field R.

The coefficient context and variable name are part of field identity. Elements are reduced fractions in the associated univariate polynomial ring, with a monic denominator.

Implementations

impl<R: Field> RationalFunctionField<R>

pub fn new( coefficient_ring: R, variable: impl Into<String>, ) -> Result<Self, RationalFunctionError>

Construct coefficient_ring(variable).

pub fn coefficient_ring(&self) -> &R

Coefficient field.

pub fn variable(&self) -> &str

Name of the transcendental generator.

pub fn polynomial_ring(&self) -> &PolynomialRing<R>

Associated univariate polynomial ring.

pub fn to_json(&self) -> Result<String, NoetherError>

where R: Serialize,

Serialize the complete coefficient-field and variable context.

pub fn from_json(value: &str) -> Result<Self, NoetherError>

where R: for<'de> Deserialize<'de>,

Deserialize and revalidate a rational-function field context.

pub fn generator(&self) -> RationalFunction<R>

Transcendental generator.

pub fn constant( &self, coefficient: R::Element, ) -> Result<RationalFunction<R>, RationalFunctionError>

Embed one coefficient as a constant rational function.

pub fn from_polynomial( &self, polynomial: Polynomial<R>, ) -> Result<RationalFunction<R>, ContextMismatchError>

Embed one polynomial from the associated univariate polynomial ring.

pub fn fraction( &self, numerator: Polynomial<R>, denominator: Polynomial<R>, ) -> Result<RationalFunction<R>, RationalFunctionError>

Construct and canonically reduce numerator / denominator.

Trait Implementations

impl<R: Clone + Field> Clone for RationalFunctionField<R>

fn clone(&self) -> RationalFunctionField<R>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<R: Field> Debug for RationalFunctionField<R>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'de, R> Deserialize<'de> for RationalFunctionField<R>

where R: Field + Deserialize<'de>,

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<R: Field> Display for RationalFunctionField<R>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<R: Field> Field for RationalFunctionField<R>

fn inverse( &self, value: &Self::Element, ) -> Result<Self::Element, InversionError>

Invert a nonzero value in this context.

impl<R: Field> PartialEq for RationalFunctionField<R>

fn eq(&self, other: &Self) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<R: Field> Ring for RationalFunctionField<R>

type Element = RationalFunction<R>

Elements manufactured and validated by this context.

fn contains(&self, value: &Self::Element) -> bool

Test whether a value belongs to this exact context.

fn zero(&self) -> Self::Element

The additive identity in this context.

fn one(&self) -> Self::Element

The multiplicative identity in this context.

fn add( &self, a: &Self::Element, b: &Self::Element, ) -> Result<Self::Element, ContextMismatchError>

Add two elements after checking their context.

fn sub( &self, a: &Self::Element, b: &Self::Element, ) -> Result<Self::Element, ContextMismatchError>

Subtract two elements after checking their context.

fn mul( &self, a: &Self::Element, b: &Self::Element, ) -> Result<Self::Element, ContextMismatchError>

Multiply two elements after checking their context.

fn neg( &self, value: &Self::Element, ) -> Result<Self::Element, ContextMismatchError>

Negate an element after checking its context.

fn is_zero(&self, value: &Self::Element) -> bool

Test whether a value is the additive identity.

fn sum_products( &self, products: &[(&Self::Element, &Self::Element)], ) -> Result<Self::Element, ContextMismatchError>

Compute a sum of pairwise products in this context.

impl<R: Field> SemanticType for RationalFunctionField<R>

const TYPE_ID: &'static str = "noether/commalg/RationalFunctionField@1"

Versioned, language-neutral semantic identity.

fn canonical_bytes(&self) -> Result<Vec<u8>, NoetherError>

Serialize without backend- or language-specific identity.

fn describe() -> &'static TypeDescription

Return static discovery metadata for the type.

impl<R> Serialize for RationalFunctionField<R>

where R: Field + Serialize,

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

impl<R: Field> UnitInversion for RationalFunctionField<R>

fn inverse_unit( &self, value: &Self::Element, ) -> Result<Self::Element, UnitError>

Invert value when it belongs to this context and is a unit.

impl<R: Field> CommutativeRing for RationalFunctionField<R>

impl<R: Field> Eq for RationalFunctionField<R>

impl<R: Field> IntegralDomain for RationalFunctionField<R>